(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.

r = 9sin(θ)

θ = pi/6

2. Relevant equations

dy/dx = (dy/dθ) / (dx/dθ)

x=rcosθ

y=rsinθ

(sinx)^2 = (1/2)(1-cos2x)

(cosx)^2 = (1/2)(1+cos2x)

2sinxcosx = sin(2x)

3. The attempt at a solution

r = 9sin(θ)

x=rcos(θ)=9sin(θ)cos(θ)= --> Would this be sin(9θ) or sin(18θ)?

y=rsin(θ)=9sin(θ)sin(θ)= 9sin^2(θ)

dy/dx = (dy/dθ) / (dx/dθ) = (9 * 9sinθcosθ) / (cos(18θ) * 9) = sin(18θ)/cos(18θ) = tan(18θ)

θ = pi/6

tan(18*pi/6)=tan(3pi)=0

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# Homework Help: Find Tangent Slope with Polar coordinates

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